Global existence from single-component $L_{p}$ estimates in a semilinear reaction-diffusion system
Authors:
Pavol Quittner and Philippe Souplet
Journal:
Proc. Amer. Math. Soc. 130 (2002), 2719-2724
MSC (1991):
Primary 35B60, 35K50, 35K60
DOI:
https://doi.org/10.1090/S0002-9939-02-06453-5
Published electronically:
February 4, 2002
MathSciNet review:
1843418
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: For a system of two reaction-diffusion equations coupled by power nonlinearities, we prove that an $L_{p}$ bound on a single component for suitable $p$ is enough to guarantee global existence. Also we provide a strong indication that our condition on $p$ is the best possible. Moreover, this continuation result is in contrast with the corresponding necessary and sufficient conditions for local existence obtained earlier by the authors.
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Additional Information
Pavol Quittner
Affiliation:
Institute of Applied Mathematics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia
Email:
quittner@fmph.uniba.sk
Philippe Souplet
Affiliation:
Département de Mathématiques, INSSET, Université de Picardie, 02109 St-Quentin, France – and – Laboratoire de Mathématiques Appliquées, UMR CNRS 7641, Université de Versailles, 45 avenue des Etats-Unis, 78035 Versailles, France
MR Author ID:
314071
Email:
souplet@math.uvsq.fr
Received by editor(s):
April 20, 2001
Published electronically:
February 4, 2002
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2002
American Mathematical Society